Question

Let P, q and 3 be respectively the first, third and fifth terms of an AP. Let d be the common difference. If the product (pa) is minimum, then what is the value of d?​
a. 1
b. 3/8
c. 9/8
d. 9/4

Answer 1

Answer:

Step-by-step explanation:

9(25a  

2

+b  

2

)+25(c  

2

−3ac)=15b(3a+c)

225a  

2

+9b  

2

+25c  

2

−75ac=45ab+15bc

225a  

2

+9b  

2

+25c  

2

−75ac−45ab−15bc=0

(15a)  

2

+(2b)  

2

+(5c)  

2

−(15a)(5c)−(15a)(3b)−(3b)(5c)=0

(15a)  

2

+(2b)  

2

+(5c)  

2

=(15a)(5c)+(15a)(3b)+(3b)(5c)

15a=3b=5c=k

b=5a and c=3a

Hence, a=  

15

k

​

, b=  

3

k

​

 and c=  

5

k

​

 

∴b−a=  

15

4k

​

 

and c−a=  

15

2k

​

 

and b−c=  

15

2k

​

 

∴c−a=b−c

⇒2c=a+b

Hence, b,c and a are in A.P.

Answer 2

Answer:

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